Sequential monoscopic tracking

ABSTRACT

A method of sequential monoscopic tracking is described. The method includes generating a plurality of projections of an internal target region within a body of a patient, the plurality of projections comprising projection data about a position of an internal target region of the patient. The method further includes generating external positional data about external motion of the body of the patient using one or more external sensors. The method further includes generating, by a processing device, a correlation model between the projection data and the external positional data by fitting the plurality of projections of the internal target region to the external positional data. The method further includes estimating the position of the internal target region at a later time using the correlation model.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/482,135, filed Apr. 5, 2017 and of U.S. ProvisionalPatent Application No. 62/482,604, filed Apr. 6, 2017, the entirecontents of both of which are hereby incorporated by reference.

TECHNICAL FIELD

Embodiments of the present disclosure relate to tracking a position of atarget using data from x-ray imagers.

BACKGROUND

In radiation treatment, doses of radiation delivered via a radiationtreatment beam from a source outside a patient's body are delivered to atarget region in the body, in order to destroy tumorous cells.Typically, the target region consists of a volume of tumorous tissue.During radiation treatment, care must be taken to track movement of thetarget region, so that treatment doses of the radiation treatment beamare directed to the intended area of the patient's body.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present disclosure are illustrated by way of example,and not by way of limitation, in the figures of the accompanyingdrawings.

FIG. 1A illustrates a radiation treatment system that may be used inaccordance with embodiments described herein.

FIG. 1B is a cross-section of the radiation treatment system inaccordance with embodiments described herein.

FIG. 2A illustrates a volumetric imaging device and a projection, inaccordance with embodiments described herein.

FIG. 2B illustrates a projection image, in accordance with embodimentsdescribed herein.

FIG. 3 is a diagram illustrating the internal markers in combinationwith an external marker to track the motion of the target region,according to embodiments.

FIG. 4A is a flowchart illustrating a method for compensating forbreathing and other motion in a treatment system, according toembodiments.

FIG. 4B is a first flowchart illustrating a method for sequentialmonoscopic tracking in a treatment system, according to embodiments.

FIG. 4C is a second flowchart illustrating a method for sequentialmonoscopic tracking in a treatment system, according to embodiments.

FIG. 4D is a third flowchart illustrating a method for sequentialmonoscopic tracking in a treatment system, according to embodiments.

FIG. 5 illustrates a portal imaging radiation treatment system, inaccordance with embodiments described herein.

FIG. 6 illustrates a gantry based intensity modulated radiationtreatment system, in accordance with embodiments described herein.

FIG. 7 illustrates a helical radiation delivery system, in accordancewith embodiments described herein.

FIG. 8 illustrates examples of different systems that may be used in thegenerating of the performing of radiation treatment, in accordance withembodiments described herein.

DETAILED DESCRIPTION

Described herein are embodiments of methods and apparatus for sequentialmonoscopic tracking. Embodiments of the present disclosure may be usedwith a radiation treatment delivery system such as the CyberKnife®radiosurgery system that includes stereo x-ray imaging capability.Alternatively, other types of radiation treatment delivery systems(e.g., gantry based, helical based, etc.) may be used.

In one embodiment, a radiation treatment system includes a linearaccelerator (LINAC) 1201 that acts as a radiation treatment source. Itis important to ensure that during treatment, any movement of a targetregion of patient is carefully tracked so that doses of radiationtreatment are directed to the intended target. A sequential monoscopictracking system, such as that described herein, would therefore bedesirable in radiation treatment systems such as the CyberKnife®radiation treatment system.

The use of a volumetric imaging system (e.g., the medPhoton ImagingRingSystem (IRS)) with a radiation treatment delivery system (e.g., theCyberKnife® radiation treatment system) as shown in FIG. 1A enables newimage registration and image tracking opportunities. For example, inembodiments of the present disclosure, such systems may acquire two ormore flat-panel X-ray images using only a single imager.

Embodiments of the present disclosure track the 3D position of a targetinside a patient using data from x-ray images acquired sequentially fromtwo or more flat-panel X-ray images acquired at different times. Suchimaging may be referred to as sequential monoscopic imaging becausesingle (monoscopic) images are taken sequentially (e.g., several secondsapart) from different angles. In some embodiments, images may be takenbetween once every second to once every minute, inclusive. In otherembodiments, images may be taken between once every 100 milliseconds toonce every two minutes, inclusive. A distinction from the stereo x-rayimaging is that a single monoscopic image does not fully define theposition of the target in 3D space. An object visualized in a singlex-ray image lies somewhere on a line that connects the x-ray source andthe position of the object in the x-ray image.

Information about the object position from a sequence of individualimages acquired from different positions may be fitted to a correlationmodel simultaneously to estimate the most likely trajectory of thetarget over the observed period. The correlation between a moving 3Dtarget position and an externally detected breathing amplitude may bemodeled using projections acquired from multiple individual flat-panelX-ray images (e.g., monoscopic projection images), all acquired atdifferent times and from at least two different positions. Using themathematical formulae described herein, the monoscopic projection imagesmay be fitted to a 3D model to estimate the trajectory of the targetover a period of time

In one embodiment, a projection (also referred to herein as a“projection image”) may be an image depicting the internal region in abody projected to a plane (2D) outside the body from a single viewingangle. In this embodiment, an X-ray point source and a flat paneldetector on opposite sides of the body may be used to acquire aprojection image. The X-ray source and detector may be mounted on a ringgantry that rotates around the body, allowing projection images to beacquired from a variety of imaging angles.

In another embodiment, projection data may include both the linesbetween the 2D detector positions of the internal target and the x-raypoint source, and/or the 2D detector positions themselves. In oneembodiment, a correlation model between the 3D target position and theexternal sensor position may be fit by minimizing the distance betweenthe model projected to the detector and the 2D detector positions,and/or by minimizing the distance between the model and the linesbetween the 2D detector positions and the x-ray point source.

For example, a correlation model may be generated by fitting the 2Dtarget positions acquired at multiple time points to simultaneouslyacquired external measurements (e.g., external marker positions). Such acorrelation model can be used for example in a radiation therapy system.In such a system, the correlation model can be generated beforetreatment; during treatment, the internal tumor position is estimatedfrom the external measurements using the correlation model, and thisinformation is used to move or shape the radiation beam dynamically withthe target.

The term “target” may refer to one or more fiducials near (within somedefined proximity to) a treatment area (e.g., a tumor). In anotherembodiment a target may be a bony structure. In yet another embodiment atarget may refer to soft tissue (e.g., tumor) of a patient. A target maybe any defined structure or area capable of being identified andtracked, as described herein.

FIG. 1A illustrates a radiation treatment system 1200 that may be usedin accordance with embodiments described herein. As shown, FIG. 1Aillustrates a configuration of a radiation treatment system 1200. In theillustrated embodiments, the radiation treatment system 1200 includes alinear accelerator (LINAC) 1201 that acts as a radiation treatmentsource. In one embodiment, the LINAC 1201 is mounted on the end of arobotic arm 1202 having multiple (e.g., 5 or more) degrees of freedom inorder to position the LINAC 1201 to irradiate a pathological anatomy(e.g., target 1225) with beams delivered from many angles, in manyplanes, in an operating volume around a patient. Treatment may involvebeam paths with a single isocenter, multiple isocenters, or with anon-isocentric approach. Alternatively, other types of image guidedradiation treatment (IGRT) systems may be used. In one alternativeembodiment, the LINAC 1201 may be mounted on a gantry based system asdescribed below.

LINAC 1201 may be positioned at multiple different nodes (predefinedpositions at which the LINAC 1201 is stopped and radiation may bedelivered) during treatment by moving the robotic arm 1235. At thenodes, the LINAC 1201 can deliver one or more radiation treatment beamsto a target. The nodes may be arranged in an approximately sphericaldistribution about a patient. The particular number of nodes and thenumber of treatment beams applied at each node may vary as a function ofthe location and type of pathological anatomy to be treated.

The radiation treatment system 1200 includes an imaging system 1210having a processing device 1230 connected with x-ray sources 1203A and1203B (i.e., imaging sources) and fixed x-ray detectors 1204A and 1204B.Alternatively, the x-ray sources 103A, 1203B and/or x-ray detectors1204A, 1204B may be mobile, in which case they may be repositioned tomaintain alignment with the target 120, or alternatively to image thetarget from different orientations or to acquire many x-ray images andreconstruct a three-dimensional (3D) cone-beam CT. In one embodiment,the x-ray sources are not point sources, but rather x-ray source arrays,as would be appreciated by the skilled artisan. In one embodiment, LINAC1201 serves as an imaging source, where the LINAC power level is reducedto acceptable levels for imaging.

Imaging system 1210 may perform computed tomography (CT) such as conebeam CT or helical megavoltage computed tomography (MVCT), and imagesgenerated by imaging system 1210 may be two-dimensional (2D) orthree-dimensional (3D). The two x-ray sources 1203A and 1203B may bemounted in fixed positions on the ceiling of an operating room and maybe aligned to project x-ray imaging beams from two different angularpositions (e.g., separated by 90 degrees) to intersect at a machineisocenter (referred to herein as a treatment center, which provides areference point for positioning the patient on a treatment couch 1206during treatment) and to illuminate imaging planes of respectivedetectors 1204A and 1204B after passing through the patient. In oneembodiment, imaging system 1210 provides stereoscopic imaging of atarget and the surrounding volume of interest (VOI). In otherembodiments, imaging system 1210 may include more or less than two x-raysources and more or less than two detectors, and any of the detectorsmay be movable rather than fixed. In yet other embodiments, thepositions of the x-ray sources and the detectors may be interchanged.Detectors 1204A and 1204B may be fabricated from a scintillatingmaterial that converts the x-rays to visible light (e.g., amorphoussilicon), and an array of CMOS (complementary metal oxide silicon) orCCD (charge-coupled device) imaging cells that convert the light to adigital image that can be compared with a reference image during animage registration process that transforms a coordinate system of thedigital image to a coordinate system of the reference image, as is wellknown to the skilled artisan. The reference image may be, for example, adigitally reconstructed radiograph (DRR), which is a virtual x-ray imagethat is generated from a 3D CT image based on simulating the x-ray imageformation process by casting rays through the CT image.

IGRT delivery system 1200 also includes a secondary imaging system 1239.Imaging system 1239 is a Cone Beam Computed Tomography (CBCT) imagingsystem, for example, the medPhoton ImagingRing System. Alternatively,other types of volumetric imaging systems may be used. The secondaryimaging system 1239 includes a rotatable gantry 1240 (e.g., a ring)attached to an arm and rail system (not shown) that move the rotatablegantry 1240 along one or more axes (e.g., along an axis that extendsfrom a head to a foot of the treatment couch 1206. An imaging source1245 and a detector 1250 are mounted to the rotatable gantry 1240. Therotatable gantry 1240 may rotate 360 degrees about the axis that extendsfrom the head to the foot of the treatment couch. Accordingly, theimaging source 1245 and detector 1250 may be positioned at numerousdifferent angles. In one embodiment, the imaging source 1245 is an x-raysource and the detector 1250 is an x-ray detector. In one embodiment,the secondary imaging system 1239 includes two rings that are separatelyrotatable. The imaging source 1245 may be mounted to a first ring andthe detector 1250 may be mounted to a second ring. In one embodiment,the rotatable gantry 1240 rests at a foot of the treatment couch duringradiation treatment delivery to avoid collisions with the robotic arm1202.

As shown in FIG. 1A, the image-guided radiation treatment system 1200may further be associated with a treatment delivery workstation 150. Thetreatment delivery workstation may be remotely located from theradiation treatment system 1200 in a different room than the treatmentroom in which the radiation treatment system 1200 and patient arelocated. The treatment delivery workstation 150 may include a processingdevice (which may be processing device 1230 or another processingdevice) and memory that modify a treatment delivery to the patient 1225based on a detection of a target motion that is based on one or moreimage registrations, as described herein.

In some embodiments, a gantry system with a helical delivery may be usedto rotate the imaging system 1210. For example, the gantry system may beused to acquire two, three, or more images (e.g., x-ray images) atdifferent angles. The radiation treatment delivery system may alsoinclude a rotational imaging system 1240 that is positioned around thepatient.

In one implementation, the system 1200 includes a frameless roboticradiosurgery system (e.g., CyberKnife® treatment delivery system). Inanother implementation, the system 1200 is coupled to a gantry-basedLINAC treatment system where, for example, LINAC 1201 is coupled to agantry of a gantry based system. Alternatively, system 1200 may be usedwith other types of radiation treatment systems, for example, a helicaldelivery system as discussed below.

FIG. 1B illustrates the configuration of an image-guided radiationtreatment (IGRT) system 700. In general, the IGRT system 700 maycorrespond to the radiation treatment system 1200 of FIG. 1A.

As shown in FIG. 1B, the IGRT system 700 may include to kilovoltage (kV)imaging sources 702A and 702B that may be mounted on tracks 722A and722B on the ceiling 720 of an operating room and may be aligned toproject imaging x-ray beams 704A, 704B, 706A, and 706B from twodifferent positions such that a ray 712A of beam 704A intersects with aray 712B of beam 704B at an imaging center 726 (i.e., isocenter), whichprovides a reference point for positioning the LINAC 708 to generatetreatment beams 716A, 716B and 716C and the patient 710 on treatmentcouch 714 during treatment. After passing through the patient 710,imaging x-ray beams 704A and 704B may illuminate respective imagingsurfaces of x-ray detectors 724A and 724B, which may be mounted at ornear the floor 718 of the operating room and substantially parallel toeach other (e.g., within 5 degrees). The kV imaging sources 702A and702B may be substantially coplanar such that the imaging surfaces of kVimaging sources 702A and 702B form a single imaging plane. In oneembodiment, kV imaging sources 702A and 702B may be replaced with asingle kV imaging source. Once an x-ray image of the patient 710 hasbeen generated, the LINAC 708 may rotate to generate a treatment beam716 from a different angle. While the LINAC 708 rotates to the differentangle, the kV imaging sources 702A and 702B may move along tracks 722Aand 722B to generate x-ray images of the patient 710 from a new angle.

FIG. 2A illustrates a volumetric imaging device 202 and a projection208, in accordance with embodiments described herein. In one embodiment,the volumetric imaging device includes a source 204 and a detector 206.In one embodiment, the source 204 and detector 206 of the volumetricimager 202 may be used during radiation treatment to track a target andalign a patient. In one embodiment, the volumetric imaging device 202may be used to take a series of images, which may be used to perform thetracking and aligning. In another embodiment, the volumetric imagingdevice 202 may be used in combination with a second imager, such as astatic 2D x-ray imager (e.g., 209), to perform the tracking andaligning. In one embodiment, a projection (e.g., a projection line) 208is shown extending from the source 204 to the detector 206.

In one embodiment, projection data (e.g., from a projection image basedon the projection line 208) may include both the lines 208 between the2D detector 206 positions and the x-ray point source 204 and the 2Ddetector 206 positions themselves. Projection image 210 of FIG. 2B isone example of a projection image. The projection image 210 shows the 2Dprojection of simulated internal structures of a patient including ribs212, a spine 214, mediastinum 218 (indicated by the dark region), and alung tumor 216. In one embodiment, a correlation model may be fit byminimizing the distance between the model projected to the detector 206and the 2D detector positions, and/or by minimizing the distance betweenthe model and the lines 208 between the 2D detector 206 positions andthe x-ray point source 204.

In one embodiment, a projection may be generated by any method ofmapping 3D points to points in a 2D plane. For example, an x-ray pointsource 204 and a flat panel detector 206 may be mounted on the rotatableplatform or gantry 202 on opposite sides of a body to acquire x-rayprojection images of the body from various angles. Each image pixel hasa scalar intensity value, which is approximately the integral of thelinear attenuation coefficients encountered along the x-ray as ittravels in a line 208 from the x-ray point source 204 to the detector206. The x-ray imaging system projects 3D positions of internal bodyanatomy to 2D positions in the x-ray projection images. In thisembodiment, internal positional data identifying a position of aninternal target region of the patient may be 3D positions. As describedherein, projections (or projection data) may refer to both the 2Dpositions in the x-ray projection images, and the lines 208 between thex-ray point source 204 and the 2D positions in the x-ray projectionimages.

FIG. 3 is a diagram illustrating a target (e.g., tumor) 151 within apatient's body 150 having internal markers 152 in combination with oneor more external markers 180 attached to the skin of the patient. Theone or more external markers 180 that are attached to the skin of thepatient permit the motion 182,154 of the abdomen or chest wall to bedetermined. In the example of the breathing of a patient, the externalmarker may track the external motion as the patient inhales and exhales.The external markers 180 may be automatically tracked via an externaldetection device with a number of optical methods, such as infrared orvisible light, and the position of the external marker may be determinedmore than 60 times per second. The external markers may also be attachedto a belt, a flexible ring or a vest which fits around the waist of thepatient.

In one embodiment, if only external markers are used to compensate forthe motion of the patient, they may not accurately reflect the internalmotion of the target organ since the target organ may move a smallamount while the external marker may move a larger amount and viceversa. Furthermore, the primary axis of motion of an external marker isnot necessarily the same as the primary axis of the internal target'smotion. For example, a lung target may have a primary axis of motion inthe patient inferior/superior direction, while an external chest markermay have a primary axis of motion in the anterior/posterior direction.The external markers alone may not be sufficiently precise to compensatefor the motion of the patient. The combination of the internal markersand the external markers may be used to accurately track the motion ofthe target organ. The periodic X-ray imaging (e.g., via an internaldetection device) of the internal markers may be correlated with thecontinuous optical tracking of the external markers (via an externaltracking device) to provide accurate tracking of the motion of thetarget organ. In order to correlate the motion of the internal andexternal markers, the relationship between the positions of the internaland external markers may be determined, which may occur at the start ofthe treatment process and will be described below with reference to FIG.4A-4D. It should be noted that in one embodiment, the Synchrony®respiratory tracking system may be used. Alternatively, other types oftracking systems may be used.

FIG. 4A is a flowchart illustrating a method 404 for compensating forchanges in the position of a target (e.g., tumor) within a patient forbreathing and/or other motion of the patient during radiation treatmentdelivery. In general, the method 404 may be performed by processinglogic that may include hardware (e.g., processing device, circuitry,dedicated logic, programmable logic, microcode, hardware of a device,etc.), software (e.g., instructions run or executed on a processingdevice), or a combination thereof. In some embodiments, the method 404may be performed by processing logic of the radiation treatment system1200 of FIG. 1.

In one embodiment, the first few operations in the method may beperformed at a time prior to the actual treatment of the patient. Inparticular, a surgeon may insert (e.g., establish) a set of internalmarkers (e.g., fiducials) in the proximity of or within the target organduring a short surgical procedure in block 406 and then, just prior totreatment, the surgeon may attach (e.g., establish) a set of externalmarkers to the chest or abdominal wall of the patient near the targetorgan in block 408. In one embodiment, the external marks may be opticalmarkers in an optical-based system. In another embodiment, other markersmay be used. In some embodiments, the target (e.g., a fiducial, softtissue, bone, etc.) may be tracked without the set of internal markersbeing inserted. Next, a processor, such as processor 602 of FIG. 8, ofthe radiation treatment device that receives positional information ofthe internal and external markers correlates the position of theinternal markers and the external markers in block 410 just prior tostarting the treatment of the patient. The method for correlating theinternal markers with the external markers is described below. Once thepositions of the internal and external markers have been correlated, thetreatment of the patient may begin.

In one embodiment, the processing device of the radiation treatmentsystem determines if the total elapsed time since the last time theinternal markers were imaged is equal to a predetermined time period atblock 411. The predetermined time period may be, for example, on theorder of a few seconds. Alternatively, other time periods may be used.If the total elapsed time is equal to the predetermined time period,then the treatment beam is deactivated and the internal markers areimaged using, for example, x-ray imaging in block 416. In anotherembodiment, the treatment beam is not deactivated during the acquisitionof new x-ray images. Next, the total elapsed time is reset to zero atblock 418 and the method returns to block 411. Returning to block 411,if the total elapsed time is not equal to the predetermined time period,then the external markers are tracked in block 412 while the treatmentbeam is activated (e.g., the treatment delivery system is controlled) inblock 414. The external markers may be tracked so that position data isprovided to the processing device of the radiation treatment system, forexample, sixty times per second. Alternatively, other time periods maybe used. In some embodiments, the system may take x-ray images when therotating gantry reaches predetermined angles. For example, an x-rayimage may be taken every time the gantry passes 0 degrees and 90 degreeson each rotation. In other embodiments, a combination of time periodsand angles may be used. The processing device may then correlate theposition of the external markers with the internal markers and generatepositional data about any change in the position of the target organ.Thus, between the periodic imaging of the internal markers, the positionof the external markers is used to track the position of the target.

When movement of the target is detected, the radiation treatment systemmay compensate for the movement to control the radiation treatmentdelivery in a number of different ways. For example, the treatmentsystem may move the LINAC and/or move the patient treatment couch tocontrol the direction of the treatment beam relative to the target. Thetreatment system may turn the radiation treatment beam on or off to becoincident with the target. The treatment system may also shape orcollimate the radiation treatment beam, modify the beam energy, orotherwise change the characteristics of the radiation treatment beam.

Embodiments of the present disclosure enable tracking the 3D position ofthe target inside the patient using data from two or more flat-panelX-ray images acquired at different times. The correlation between themoving internal 3D target position and the externally detected motion(e.g., breathing) amplitude is modeled using data acquired from multipleindividual flat-panel X-ray images, all acquired at different times.Various mathematical approaches to sequential monoscopic tracking (SMT)may be used, two of which are discussed below. However, the presentdisclosure is not limited to only the two approaches discussed below. Inalternative embodiments, other mathematical approaches may be used.

In one embodiment, the mathematical approach can be visualized asprojecting lines from the X-ray source, through the (to be determined)target position model, onto the panel, and using linear algebra to solvefor a target position model that minimizes the sum-of-least-squaresdifference between the projected model positions and the actualpositions detected in 2-D on the panel (hereinafter referred to as“projecting lines approach”). The model can be a single static tumorposition (for quasi-static tracking), or can be a function of breathingamplitude (for respiratory tracking). The projecting lines mathematicalapproach is described below for (1) a helical radiation treatmentdelivery system with non-static target motion modeling (e.g., due torespiration or cardiac motion), (2) a helical radiation treatmentdelivery system with quasi-static target motion modeling; and (3) aradiation treatment delivery system, having a target motion trackingsystem, with non-static target motion modeling. However, the presentdisclosure is not limited to only the approaches discussed below. Inalternative embodiments, other mathematical approaches may be used.

The mathematical approach discussed in this section may be in referenceto a helical radiation delivery system such as the helical deliverysystem referenced herein. In cases (generally lung, liver, pancreas,breast, and renal treatments) where the target is expected to undergosignificant respiratory motion, instead of using pairs of images toperform periodic correction, a model is built that allows real-timecompensation for target motion. The first input to this model is astream of 3D positions of external fiducials, or markers, on a vest wornby the patient. An example of external markers may be LEDs on the vestthat are tracked, for example, at approximately 30 frames a second. Thesecond input is periodic data from the imaging system, for example asingle projection X-ray image. Specifically, each time an image istaken, the fiducials (fiducial treatments) or the target are localizedin the X-ray image, with the help of a Digitally ReconstructedRadiograph (DRR) which uses the planning computerized tomography (CT) tosimulate an X-ray projection at the desired angle. From the localizationstep, it is possible to deduce the line joining the X-ray source to thefiducial (or target) centroid. This line, together with the sourceposition, is then the second input to the correlation model.

In the instance of a target being in the image, finding the line joiningsource to target is trivial: it is simply the line joining the source tothe centroid of the target as identified on the detector plane. For thecase involving multiple fiducials, however, taking the centroid of thefiducial constellation in the detector plane, and the line from this tothe source, would give an incorrect result because the fiducials may beat different distances from the source.

One cannot derive exactly the fiducials' distances from the source in asingle projection image, so instead we approximate the distances usingthe known 3D locations of the fiducials at nominal alignment. In someembodiments, each fiducial may be tracked individually and a 3D modelcorresponding to each tracked fiducial may be generated.

Writing x_(j) as the positions of the fiducials at nominal alignment,j=1 . . . N, S as the position of the source, and ƒ_(j) as the 3Dprojections of the fiducials onto the detector plane (the 2D positionsare determined by the localization algorithm, and a 3D projection iscalculated by giving each fiducial an arbitrary “depth” corresponding tothe detector), we estimate the 3D position P_(j) of each fiducial as theclosest point to x_(j) on the line S+λ(ƒ_(j)−S). Specifically, we knowthatP _(j) =S+λ(ƒ_(j) −S)And also that P_(j) lies on the perpendicular to the line from x_(j),i.e.,(x _(j) −P _(j))·(ƒ_(j) −S)=0Solving these equations together gives

$\lambda = \frac{\left( {x_{j} - S} \right) \cdot \left( {f_{j} - S} \right)}{\left( {f_{j}\mspace{31mu} S} \right) \cdot \left( {f_{j}\mspace{31mu} S} \right)}$which allows us to estimate P_(j), and thus take the mean value as theestimated centroid of the fiducial configuration. This position, inaddition to the source, then defines the line which is sent to themodeler.

For embodiments in which the target does not experience significantrespiratory and/or cardiac motion, it may be desirable to be able toperform periodic corrections for target translation, and to measuretarget rotation in order to ensure that it stays within acceptablebounds. To do this, pairs of images may be used; generally these will bethe two most recent images taken with the gantry rotating, subject tosome restrictions (e.g., the angle separation between the two imagesshould be at least 30, and no more than 150 degrees).

Because the images taken with the kV snapshot imaging system on thegantry also share an inferior/superior direction, it is possible toextend the approach described above to account for angles that are notorthogonal, as with robotic based LINACs, as will be described in moredetail below. However, the couch will be undergoing continual motionthroughout treatment, and the effect of this motion on the projectedfiducial positions varies according to the distance of each fiducialfrom the X-ray source. The extension of the robotic based LINAC approachto take account of this couch motion is non-trivial, and hence analternate method is suggested.

For example, in a general case where there are N images (N would beequal to 2 if the workflow suggested above were used), and the cameraprojection matrix is allowed to vary between the images. In reality,unless flexion of the gantry causes significant change in the cameraparameters, it can be assumed that the projection matrix remainsconstant.

The standard pinhole camera projection model can be represented by aprojection matrix P where

$\begin{pmatrix}I_{x} \\I_{y} \\1\end{pmatrix} = {{\begin{pmatrix}{fk}_{u} & 0 & u_{0} & 0 \\0 & {- {fk}_{v}} & v_{0} & 0 \\0 & 0 & 1 & 0\end{pmatrix}\begin{pmatrix}x_{F} \\y_{F} \\z_{F} \\1\end{pmatrix}} = {P\begin{pmatrix}x_{F} \\y_{F} \\z_{F} \\1\end{pmatrix}}}$

F is the 3D coordinate system of the camera, f is the focal length(e.g., the distance between the X-ray source and the intersection of thesource-detector axis with the center of the detector), k_(u) and k_(v)are the inverses of the pixel dimensions along the x and y image axes,u₀ and v₀ are the image coordinates of the intersections of the opticalaxis with the imaging plane, {x_(F),y_(F),z_(F)} is the threedimensional position in the camera coordinate system of the object beingprojected, and {(I_(jx),I_(jy)} is the 2D image coordinate of the objectas it appears in the projection (the X-ray image, in this case).

Before performing projections, the position of the object may berendered from the imaging coordinate system into the camera coordinatesystem. This can be accomplished by a rigid transformation that we willlabel R_(j), with the j suffix denoting the transformation from theimaging coordinate system to the camera coordinates for image j. Then,labeling the projection matrix for image j as P_(j), we haveI _(j) =P _(j) R _(j)(x _(j) +c _(j))where c_(j)={c_(jx) c_(jy) c_(jz)}^(T) is the vector representing couchoffset at image j, x={x y z}^(T) is the position of the object in theimaging coordinate system, and I_(j)={I_(jx) I_(jy)}^(T) is the 2Dcoordinate of the projection of the object on the imaging plane. WritingT_(j) as the 3-by-4 matrix P_(j)R_(j), in homogeneous coordinates

$I_{jx} = \frac{{T_{j}^{11}\left( {x + c_{jx}} \right)} + {T_{j}^{12}\left( {y + c_{jy}} \right)} + {T_{j}^{13}\left( {z + c_{jz}} \right)} + T_{j}^{14}}{{T_{j}^{31}\left( {x + c_{jx}} \right)} + {T_{j}^{32}\left( {y + c_{jy}} \right)} + {T_{j}^{33}\left( {z + c_{jz}} \right)} + T_{j}^{34}}$and$I_{jy} = \frac{{T_{j}^{21}\left( {x + c_{jx}} \right)} + {T_{j}^{22}\left( {y + c_{jy}} \right)} + {T_{j}^{22}\left( {z + c_{jz}} \right)} + T_{j}^{24}}{{T_{j}^{31}\left( {x + c_{jx}} \right)} + {T_{j}^{32}\left( {y + c_{jy}} \right)} + {T_{j}^{33}\left( {z + c_{jz}} \right)} + T_{j}^{34}}$which can be rearranged into

${\begin{pmatrix}{{T_{j}^{31}I_{jx}} - T_{j}^{11}} & {{T_{j}^{32}I_{jx}} - T_{j}^{12}} & {{T_{j}^{33}I_{jx}} - T_{j}^{13}} \\{{T_{j}^{31}I_{jy}} - T_{j}^{21}} & {{T_{j}^{32}I_{jy}} - T_{j}^{22}} & {{T_{j}^{33}I_{jy}} - T_{j}^{23}}\end{pmatrix}\begin{pmatrix}x \\y \\z\end{pmatrix}} = \begin{pmatrix}{T_{j}^{14} + {c_{jx}\left( {T_{j}^{11} - {T_{j}^{31}I_{jx}}} \right)} + {c_{jy}\left( {T_{j}^{12} - {T_{j}^{32}I_{jx}}} \right)} + {c_{jz}\left( {T_{j}^{13} - {T_{j}^{33}I_{jx}}} \right)} - {T_{j}^{34}I_{jx}}} \\{T_{j}^{24} + {c_{jx}\left( {T_{j}^{21} - {T_{j}^{31}I_{jy}}} \right)} + {c_{jy}\left( {T_{j}^{22} - {T_{j}^{32}I_{jy}}} \right)} + {c_{jz}\left( {T_{j}^{23} - {T_{j}^{33}I_{jy}}} \right)} - {T_{j}^{34}I_{jy}}}\end{pmatrix}$In general then, for N views, the equation is

${\begin{pmatrix}{{T_{1}^{31}I_{1\; x}} - T_{1}^{11}} & {{T_{1}^{32}I_{1\; x}} - T_{1}^{12}} & {{T_{1}^{33}I_{1\; x}} - T_{1}^{13}} \\{{T_{1}^{31}I_{1\; y}} - T_{1}^{21}} & {{T_{1}^{32}I_{1\; y}} - T_{1}^{22}} & {{T_{1}^{33}I_{1\; y}} - T_{1}^{23}} \\\vdots & \vdots & \vdots \\{{T_{N}^{31}I_{Nx}} - T_{N}^{11}} & {{T_{N}^{32}I_{Nx}} - T_{N}^{12}} & {{T_{N}^{33}I_{Nx}} - T_{N}^{13}} \\{{T_{N}^{31}I_{Ny}} - T_{N}^{21}} & {{T_{N}^{32}I_{Ny}} - T_{N}^{22}} & {{T_{N}^{33}I_{Ny}} - T_{N}^{23}}\end{pmatrix}\begin{pmatrix}x \\y \\z\end{pmatrix}} = \begin{pmatrix}{T_{1}^{14} + {c_{1\; x}\left( {T_{1}^{11} - {T_{1}^{31}I_{1\; x}}} \right)} + {c_{1\; y}\left( {T_{1}^{12} - {T_{1}^{32}I_{1\; x}}} \right)} + {c_{1\; z}\left( {T_{1}^{13} - {T_{1}^{33}I_{1\; x}}} \right)} - {T_{1}^{34}I_{1\; x}}} \\{T_{1}^{24} + {c_{1\; x}\left( {T_{1}^{21} - {T_{1}^{31}I_{1\; y}}} \right)} + {c_{1\; y}\left( {T_{1}^{22} - {T_{1}^{32}I_{1\; y}}} \right)} + {c_{1\; z}\left( {T_{1}^{23} - {T_{1}^{33}I_{1\; y}}} \right)} - {T_{1}^{34}I_{1\; y}}} \\\vdots \\{T_{N}^{14} + {c_{Nx}\left( {T_{N}^{11} - {T_{N}^{31}I_{Nx}}} \right)} + {c_{Ny}\left( {T_{N}^{12} - {T_{N}^{32}I_{Nx}}} \right)} + {c_{Nz}\left( {T_{N}^{13} - {T_{N}^{33}I_{Nx}}} \right)} - {T_{N}^{34}I_{Nx}}} \\{T_{N}^{24} + {c_{Nx}\left( {T_{N}^{21} - {T_{N}^{31}I_{Ny}}} \right)} + {c_{Ny}\left( {T_{N}^{22} - {T_{N}^{32}I_{Ny}}} \right)} + {c_{Nz}\left( {T_{N}^{23} - {T_{N}^{33}I_{Ny}}} \right)} - {T_{N}^{34}I_{Ny}}}\end{pmatrix}$

As long as N>=2, the system is overdetermined, and the solution for xcan be found by means of a standard matrix minimization method: find Xto minimize ∥AX−B∥², with the general solution X=(A^(T)A)⁻¹A^(T)B.

In one embodiment, this establishes a framework by which the estimatedthree dimensional position of each fiducial marker can be found by meansof its projected locations in multiple X-ray images. It remains to usethese fiducial marker positions to estimate the 6D corrections(translations and three roll angles) necessary to map from the nominalalignment position to the current target position.

In one embodiment, this is may be a point-based registration problem.There may be closed form solutions to finding the rigid transformationthat maps one set of points to another corresponding set, such that thesum of squared distances between the points is minimized. Writing X asthe set of fiducial positions in image coordinates, and Y as thecorresponding positions at nominal alignment, the translation componentis simply X−Y, e.g., the translation that maps the centroid of Y to thecentroid of X. Writing {tilde over (X)} and {tilde over (Y)} as the two3×N matrices of fiducial coordinates each with respect to their owncentroid, and using Schönemann's solution and notation, the orthogonalmatrix R minimizing ∥R{tilde over (Y)}−{tilde over (X)}∥² is R=UV^(T),where {tilde over (X)}{tilde over (Y)}^(T)=UAV^(T) is the Singular ValueDecomposition of {acute over (X)}{tilde over (Y)}^(T). It should benoted that both Horn's and Schönemann's solutions solve for anorthogonal matrix, which includes both rotations and reflections. Amodification that allows the optimal rotation to be found may provide:in the case that the above solutions yield a reflection (i.e.,det(R)=−1), the optimal rotation may be found by taking R=USV^(T), wherein the three dimensional case

$S = {\begin{pmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & {- 1}\end{pmatrix}.}$

To derive the yaw, pitch and roll rotation angles y, p, and r thefollowing convention may be used: we assume the x axis corresponds tothe patient inferior-superior axis (and hence the axis about which thegantry rotates), the y axis corresponds to the patient left-right axis,and the z axis to the patient anterior-posterior axis. Further, weassume that the angles are applied in order yaw, pitch, and roll.Writing sy, cy, sp, cp, sr, cr as the sines and cosines of the angles,the rotation matrix comes out as

$\quad\begin{pmatrix}{{cp}\mspace{14mu}{cy}} & {{- {cp}}\mspace{14mu}{sy}} & {sp} \\{{{cr}\mspace{14mu}{sy}} + {{sr}\mspace{14mu}{sp}\mspace{14mu}{cy}}} & {{{cr}\mspace{14mu}{cy}} - {{sr}\mspace{14mu}{sp}\mspace{14mu}{sy}}} & {{- {sr}}\mspace{14mu}{cp}} \\{{{sr}\mspace{14mu}{sy}} - {{cr}\mspace{14mu}{sp}\mspace{14mu}{cy}}} & {{{sr}\mspace{14mu}{cy}} + {{cr}\mspace{14mu}{sp}\mspace{14mu}{sy}}} & {{cr}\mspace{14mu}{cp}}\end{pmatrix}$This allows us to derive the values of the angles, which are

y = tan⁻¹(−R¹²/R¹¹)$p = {\tan^{- 1}\left( {R^{13}/\sqrt{\left( R^{33} \right)^{2} + \left( R^{33} \right)^{2}}} \right)}$r = tan⁻¹(−R²³/R³³)

In the another embodiment, the imaging isocenter may be designated asthe origin of the image coordinate system. It may be assumed that thegeometry of the imaging system is well characterized, so the positionsS_(A) and S_(B) of the two X-ray sources in the imaging system areknown, and the position and orientation of the X-ray detectors areknown. Because the pixel size of the X-ray detectors is known, anydetected fiducial position can be related to a coordinate in the imagingcoordinate system lying on the detector surface.

We write as {F_(A1), F_(A2), . . . , F_(AN)} and {F_(B1), F_(B2), . . ., F_(BN)} these coordinates representing the projection of the fiducialsonto the surfaces of detectors A and B, respectively. Then the trueposition of fiducial i can be written as lying on two lines defined by:S _(A)+λ_(Ai)(F _(Ai) −S _(A))andS _(B)+λ_(Bi)(F _(Bi) −S _(B))where λ_(Ai) and λ_(Bi) are scalar parameters defining position alongthe line.

Ideally, the two lines would intersect, but because of uncertainty offiducial localization and the calibration of the imaging system,typically the two lines do not exactly coincide, so a method must befound to estimate the fiducial position using the lines. Because theinferior/superior direction is shared between the two imaging planes,reconciling the two projections is as simple as taking theinferior/superior projected fiducial position in both planes to be themean of the values from the two planes. With both projections having thesame inferior/superior position, it becomes a simple back projectionproblem to find the 3D location that represents the intersection of thetwo modified fiducial projections.

In an alternative embodiment, the mathematical approach may bevisualized as fuzzy cones projected from the source to the panel, ratherthan lines. The cones represent an uncertainty in the actual positionsdetected in 2-D by the panel. This uncertainty can be due to error inthe 2-D detection (e.g., physical limitations like pixel size, imagingprocessing limitations, etc.). Uncertainty can also be due to patientmotion between the times when images are acquired. Advantages of thisapproach in some embodiments may include: tunable parameters thatrepresent the physical and algorithmic uncertainties of the system;tunable parameters that represent expected quasi-static patient motionor rate of deviation from an existing external/internal marker motionmodel (the aging parameter—i.e., the expected standard deviation of ameasurement increases as the images age. Older images are effectivelygiven less weight; and a statistical confidence metric defined as thelikelihood of a given model explaining the measured data given thevarious tunable uncertainty parameters.

Rather than correlating breathing amplitudes with 3-D positions derivedfrom stereoscopic image pairs, embodiments of the present disclosurebuild correlation directly between the breathing amplitude and the 2-Dpositions detected in sequentially acquired flat-panel images.

An internal-external correlation model can be implemented using manydifferent functions, below are a few examples:

-   -   A linear function: āx+b, where x is the breathing amplitude and        ā and b are 3-D vectors    -   The 5-D model (A linear function of both amplitude and its first        derivative):

$\overset{\rightharpoonup}{ax} = {{\overset{\rightharpoonup}{b}\frac{dx}{dt}} + \overset{\rightharpoonup}{c}}$

-   -   A higher order polynomial model:

$\sum\limits_{i = 1}^{N}\;{\overset{\rightharpoonup}{c_{i}}x^{i}}$

-   -   Separate functions for inhalation and exhalation phases of        breathing.

Each of these functions is made up of a number of parameters. Forexample, a linear model has 6 parameters that make up its two 3-Dvectors. The 5-D model has 9 parameters, making up its three 3-Dvectors.

Generating an internal-external correlation model is a matter ofselecting the model type, and then determining values for all themodel's parameters to best fit the observed data. With simultaneouspairs of images to give us 3-D measured target positions, this can bedescribed mathematically as follows:

Let {right arrow over (p₁)}, {right arrow over (p₂)}, . . . {right arrowover (p_(m))} be 3-D target locations measured at amplitudes x₁, x₂, . .. x_(m) respectively.

Let M(x) be a model function, with n parameters c₁, c₂, . . . c_(n).

Then optimize the model parameters to minimize the sum-of-squaredifference between the modeled 3-D positions and the measured 3-Dpositions:min_(c) ₁ _(,c) ₂ _(, . . . ,c) _(n) Σ_(i=1) ^(m)(M(x _(i))− p _(i) )²

The above describes internal-external model building when the measured3-D target locations are known. In embodiments of the presentdisclosure, an internal-external correlation model is built with only2-D target locations detected in one flat-panel image at a time. Themodel generation involves an additional production of 3D model positionsto 2D positions on the flat panel detector.

-   -   Let {right arrow over (q₁)}, {right arrow over (q₂)}, . . .        {right arrow over (q_(m))} be 2-D target locations on the        flat-panel, measured at amplitudes    -   x₁, x₂, . . . x_(m) respectively.    -   Let M(x) be a model function, with n parameters c₁, c₂, . . .        c_(n).    -   Let Q_(i)({right arrow over (p)}) be a set of functions that        project 3-D points in space onto the 2-D flat-panel, for the        radiation source position and flat-panel position corresponding        to each of the m measured amplitudes.    -   Then optimize the model parameters to minimize the sum-of-square        difference between the modeled positions projected to 2-D and        the measured 2-D positions on the flat-panel: min_(c) ₁ _(, c) ₂        _(, . . . , c) _(n) Σ_(i=1) ^(m)(M(x_(i))−q_(i) )²

In one embodiment, this is the formula utilized to build a sequentialmonoscopic correlation model. In alternative embodiments, additionalembellishments may be used to make the algorithm more robust and todetect tracking errors. In one embodiment, errors in model building aredetected since sequential monoscopic modeling cannot rely on sharedmutual information found in simultaneous image pairs. Simultaneous imagepairs have one axis in common, so a discrepancy in the tracking resultsalong that axis indicate some degree of tracking error

To detect tracking errors in sequential monoscopic modeling, one caninstead provide an estimate of the expected 2-D tracking error and 3-Dpatient modeling error, and then compute statistical confidence metricsfor our model.

-   -   Let σ be the expected error between projected 2-D locations in        the model and measured 2-D locations on the flat-panel.

Change the optimization equation to be

$\min_{c_{1},c_{2},\ldots\mspace{14mu},c_{n}}{\sum\limits_{i = 1}^{m}\;\frac{\left( {{Q_{i}\left( {M\left( x_{i} \right)} \right)} - {\overset{\rightharpoonup}{q}}_{i}} \right)^{2}}{\sigma^{2}}}$

The standard deviation between the projected model and measured pointsis then

$\sqrt{\frac{1}{m}{\sum\limits_{i = 1}^{m}\;\frac{\left( {{Q_{i}\left( {M\left( x_{i} \right)} \right)} - {\overset{\rightharpoonup}{q}}_{i}} \right)^{2}}{\sigma^{2}}}}$This standard deviation between the model and measured data can be usedto test whether this model is a good fit for the data.

The model building may be made more robust to changes over time byadjusting the expected standard deviation between projected model pointsand measured 2-D positions based on the age of the measurement:

-   -   Let σ(Δt)=σ₁+σ₇Δt, where σ₁ is the constant expected error in        the 2-D position due to tracking accuracy and σ₂ is the rate at        which the expected error increases over time—called the aging        parameter.

Then optimize the model as

$\min_{c_{1},c_{2},\ldots\mspace{14mu},c_{n}}{\sum\limits_{i = 1}^{m}\;\frac{\left( {{Q_{i}\left( {M\left( x_{i} \right)} \right)} - {\overset{\rightharpoonup}{q}}_{i}} \right)^{2}}{{\sigma\left( {t_{m} - t_{i}} \right)}^{2}}}$This allows the model to use all available measurements, but moreclosely fit the newer measurements if the patient's breathing patternhas changed over time. Although embodiments of the present disclosureare described for use in modeling respiratory motion, alternateembodiments of the disclosed method and apparatus may be applied tomodeling other types of motion such as cardiac motion. In anotherembodiment, the present disclosure may also be applied to quasi-staticmotion of a target.

In another embodiment, the least-squares minimization problem to derivea 3D motion model may be:

$\min\limits_{f}{\sum\limits_{i = 1}^{n}\;{\sum\limits_{j = 1}^{m}\;{{{P_{g_{i},c_{i}}\left( {f\left( {a_{i},s_{j}} \right)} \right)} - p_{i,j}}}^{2}}}$The motion model ƒ may be optimized such that the motion of fiducialsinside the patient best matches the detected 2D fiducial locations inthe X-ray images. The pi,j may be the 2D fiducial locations in the i=1 .. . n images, for j=1 . . . m fiducials. The motion model ƒ may be afunction of the breathing amplitude ai at the time of image iacquisition and 3D fiducial position s_(j) to a motion adjusted 3Dposition s_(j)′. The function P_(gi,ci) projects the motion adjusted 3Dposition to its corresponding 2D position in the X-ray image, givengantry angle g_(i) and couch position c_(i) corresponding to image i.

In one embodiment, the system uses a fiducial detection algorithm tofind the 2D fiducial locations (p_(i,j)), then uses a solver library tosolve for the motion model in the equation above. Once an optimal modelfunction has been calculated, the 3D location of the target can bepredicted for any breathing amplitude in just a few milliseconds. In oneexample, let a be a breathing amplitude, and t be the 3D location of thetarget inside the patient without motion. Then the new 3-D targetlocation t′ is may be:t′=ƒ(a,t)

Motion models can take a variety of forms. For example, linear motionmay be modeled as ƒ(a_(i), s_(j))=[x₁,y₁,z₁]a_(i)+[x₂,y₂,z₂]+s_(j). Inthis case, the minimization process may solve for six variables(x₁,y₁,z₁,x₂,y₂,z₂) and so requires a minimum of three flat-panel imagesto construct the model. Additional images can be used to improve therobustness and statistical confidence of the model. More complex motionpaths can be modeled using alternate motion model formulae. For example,the model function could be a higher-order polynomial (e.g., cubic) tohandle non-linear target motion, or a dual-polynomial to handlehysteresis, where motion during inhalation differs from motion duringexhalation.

In one embodiment, a motion model could also include rotation or evennon-rigid spatial transforms. Models with more degrees of freedomrequire a greater minimum number of images to construct, and so requiremore additional images to reach the same level of robustness andstatistical confidence as the linear model.

In practice, a patient's breathing pattern may not remain consistentover time. The system adapts to changes in breathing pattern byre-optimizing the model whenever a new image is acquired, taking about asecond to process the image and update the model. In one embodiment,model adaptation is made more responsive to recent breathing changes byusing only the n most recent images, and giving the more recent imagesmore weight in the minimization objective function. In our formulation,weights are specified by increasing the expected error between themodeled versus predicted 2D locations, proportional to the age of theimage.

In one example, let σ represent the inherent accuracy of the 2D fiducialdetection on the panel, e.g., resulting from the finite pixel size andaccuracy of the geometric alignment of the kV imaging components. Let σ′represent an expected rate of patient breathing pattern change overtime, and Δt_(i)=t_(n)−t_(i) be the time interval between the i-th imageand the most recent (n-th) image, so Δt_(i)σ′ represents how much thebreathing pattern in the i-th image is expected to deviate from thecurrent model. The motion model minimization formula, with aging, isgiven below:

$\min\limits_{f}{\sum\limits_{i = 1}^{n}\;{\sum\limits_{j = 1}^{m}\;\left\lbrack \frac{{{P_{g_{i},c_{i}}\left( {f\left( {a_{i},s_{j}} \right)} \right)} - p_{i,j}}}{\sigma + {\Delta\; t_{i}\sigma^{\prime}}} \right\rbrack^{2}}}$

With the inclusion of aging, sequential monoscopic imaging caneffectively track non-respiratory motion as well as respiratory motion.One complication with non-respiratory motion may be that there is nocontinuous external signal, like breathing amplitude, to correlate withthe periodic X-ray images. In one embodiment, the first indication thesystem has that motion has occurred is when the next X-ray image isacquired. Advantageously, to be more responsive to target motion, thesystem may prefer position information derived from the most recentimage.

In one embodiment, to model non-respiratory motion using the modeloptimization framework above, we first define the motion model functionto be independent of breathing amplitude—for example, the functionƒ(a_(i), s_(j))=[x, y, z]+s_(j) models static translation of the 3Dtarget and fiducial positions. Second, we optimize the model using onlythe most recent few images, typically as few as only two images (e.g.,n=2). Finally, the aging parameter (σ′) may be chose to be consistentwith the speed non-respiratory targets are expected to move within thepatient—e.g., prostates have been observed to move slowly due to bladderfilling throughout treatment. Now the model minimization process canaccurately calculate the 3D position of stationary targets, andefficiently handle moving targets by preferring the position informationfrom more recent images.

In one embodiment, the model minimization framework also provides a wayto verify the consistency of the model. With stereoscopic imaging, it ispossible to compare the positions detected along the axis shared by thetwo simultaneous images to verify the tracking result. This may not bepossible with sequential monoscopic imaging. Instead, we calculate modelconfidence as the probability that the optimized motion model isconsistent with the 2D detected positions, given a priori expecteddetection accuracy (σ) and an image aging (σ′) parameter. Thisprobability may be derived by calculating the area of the chi-squareddistribution greater than the value of the optimized motion model. Thedegrees of freedom of the chi-squared distribution may be two times thenumber of 2D images times the number of fiducials (2mn). In oneembodiment, the model confidence is shown mathematically in theequations below:

$\chi_{opt}^{2} = {\sum\limits_{i = 1}^{n}\;{\sum\limits_{j = 1}^{m}\;\left\lbrack \frac{{{P_{g_{i},c_{i}}\left( {f\left( {a_{i},s_{j}} \right)} \right)} - p_{i,j}}}{\sigma + {\Delta\; t_{i}\sigma^{\prime}}} \right\rbrack^{2}}}$Model  Confidence = Pr [χ²(2 mn) > χ_(opt)²]

FIG. 4B is a first flowchart illustrating a method for sequentialmonoscopic tracking in a treatment system, according to embodiments. Ingeneral, the method 401 may be performed by processing logic that mayinclude hardware (e.g., processing device, circuitry, dedicated logic,programmable logic, microcode, hardware of a device, etc.), software(e.g., instructions run or executed on a processing device), or acombination thereof. In some embodiments, the method 401 may beperformed by processing logic of the radiation treatment system 1200 ofFIG. 1.

Beginning at block 403, processing logic may generate a plurality ofprojections of an internal target region within a body of a patient. Inone embodiment, the plurality of projections include projection dataabout a position of an internal target region of the patient (e.g., viaone or more internal detection devices). In one embodiment, theplurality of projections is sequentially acquired monoscopic projectionimages acquired using an imager (e.g., internal detection device)rotated on a gantry. In one embodiment, the plurality of projections isacquired at different points in time. The internal detection device maygenerate a single view of projection data at a time. The internaldetection device may generate a plurality of sequential images, andgenerate a single projection based on the plurality of sequentialimages. In one embodiment, the projection data identifies internalmotion of the patient's body, and the internal motion includes motion ofthe internal target region. In another embodiment, the projection dataidentifies internal motion of the patient's body, and the internalmotion includes motion of one or more implanted fiducial markers.

At block 405, processing logic generates external positional data aboutexternal motion of the body of the patient using one or more externalsensors (e.g., via one or more external detection devices). At block407, processing logic generates, by a processing device, a correlationmodel between the projection data and the external positional data. Inone embodiment, the correlation model may be generated by fitting theplurality of projections of the internal target region to the externalpositional data. In one embodiment, the correlation model identifies abest fit of an analytic function to the projection data identified inthe plurality of projections and the corresponding external positionaldata. In one embodiment, processing logic generates the correlationmodel during acquisition of a CBCT scan (or some other type of scan). Atblock 409, processing logic estimates the position of the internaltarget region at a later time using the correlation model. Processinglogic may, optionally, control the radiation treatment delivery systembased on the correlation model.

In one embodiment, to control the radiation treatment delivery systembased on the correlation model, the processing device is to direct aradiation treatment beam generated by a linear accelerator (LINAC) basedon the correlation model. In another embodiment, to control theradiation treatment delivery system based on the correlation model, theprocessing device is to control a collimator of a linear accelerator(LINAC) based on the correlation model. In one embodiment, thecollimator is a multi-leaf collimator and to control the collimator, theprocessing device is to move one or more leafs of the multi-leafcollimator. In another embodiment, to control the radiation treatmentdelivery system based on the correlation model, the processing device isto control a treatment couch. In another embodiment, to control theradiation treatment delivery system based on the correlation model, theprocessing device is to gate a radiation treatment beam generated by alinear accelerator (LINAC) based on the correlation model. In anotherembodiment, projection data corresponds to one or more fiducial markerslocated near the internal target region, and to generate the correlationmodel the processing device is to compute a deformation state of theinternal target region based on relative positions of the one or morefiducial markers.

FIG. 4C is a second flowchart illustrating a method for sequentialmonoscopic tracking in a treatment system, according to embodiments. Ingeneral, the method 402 may be performed by processing logic that mayinclude hardware (e.g., processing device, circuitry, dedicated logic,programmable logic, microcode, hardware of a device, etc.), software(e.g., instructions run or executed on a processing device), or acombination thereof. In some embodiments, the method 402 may beperformed by processing logic of the radiation treatment system 1200 ofFIG. 1.

At block 411, processing logic sequentially acquires a plurality ofx-ray images of a target using a single imager on a rotating gantry. Inone embodiment, the plurality of x-ray images is acquired by rotatingthe single imager around the target. At block 413, processing logicdetermines, by a processing device, a three dimensional position of thetarget using the sequentially acquired plurality of x-ray images. Atblock 415, processing logic optionally controls a radiation treatmentdelivery system based on the correlation model.

FIG. 4D is a third flowchart illustrating a method for sequentialmonoscopic tracking in a treatment system, according to embodiments. Ingeneral, the method 404 may be performed by processing logic that mayinclude hardware (e.g., processing device, circuitry, dedicated logic,programmable logic, microcode, hardware of a device, etc.), software(e.g., instructions run or executed on a processing device), or acombination thereof. In some embodiments, the method 404 may beperformed by processing logic of the radiation treatment system 1200 ofFIG. 1.

At block 417, processing logic generates positional data about a targetposition internal to the body of the patient. In one embodiment,processing logic generates the positional data by generating a pluralityof projections of the internal target position. At block 419, processinglogic generates external positional data about external motion of thebody of the patient using one or more external sensors. In oneembodiment, the external positional data is continuously generated,wherein “continuously” is used to mean that the external positional datais generated more frequently than “periodically” generated projections.For example, continuously generated external data could mean externalposition data generated at 30 Hz; while periodically generatedprojection data could be generated once every 30 seconds; or similarlydiscrepant time intervals, where “continuously” generated data isgenerated orders of magnitude more frequently than “periodically”generated data. At block 421, processing logic generates, by aprocessing device, a correspondence between the position of the internaltarget position and the external sensors by fitting a correlation modelto the plurality of projections of the internal target position and theexternal positional data. Optionally, the internal positional datacorresponds to one or more fiducial markers located near the internaltarget region and at block 423, processing logic computes a deformationstate of the internal target region based on relative positions of theone or more fiducial markers, to generate the correlation model. Atblock 425, processing logic controls a treatment delivery system todirect radiation towards the position of the internal target position ofthe patient based the correlation model to compensate for motions of thepatient.

Embodiments of the present disclosure may be implemented in a portalimaging system 1400 as shown in FIG. 5. In one embodiment, in the portalimaging system 1400 the beam energy of a LINAC may be adjusted duringtreatment and may allow the LINAC to be used for both x-ray imaging(e.g., generating the monoscopic images) and radiation treatment. Inanother embodiment, the system 1400 may include an onboard kV imagingsystem to generate x-ray images (e.g., monoscopic images) and a separateLINAC to generate the higher energy therapeutic radiation beams. Thesystem 1400 includes a gantry 1410, a LINAC 1420 and a portal imagingdetector 1450. The gantry 1410 may be rotated to an angle correspondingto a selected projection and used to acquire an x-ray image of a VOI ofa patient 1430 on a treatment couch 1440. In embodiments that include aportal imaging system, the LINAC 1420 may generate an x-ray beam thatpasses through the target of the patient 1430 and are incident on theportal imaging detector 1450, creating an x-ray image of the target.After the x-ray image of the target has been generated, the beam energyof the LINAC 1420 may be increased so the LINAC 1420 may generate aradiation beam to treat a target region of the patient 1430. In anotherembodiment, the kV imaging system may generate an x-ray beam that passesthrough the target of the patient 1430, creating an x-ray image of thetarget. In some embodiments, the portal imaging system may acquireportal images during the delivery of a treatment. The portal imagingdetector 1450 may measure the exit radiation fluence after the beampasses through the patient 1430. This may enable internal or externalfiducials or pieces of anatomy (e.g., a tumor or bone) to be localizedwithin the portal images.

Alternatively, the kV imaging source or portal imager and methods ofoperations described herein may be used with yet other types ofgantry-based systems. In some gantry-based systems, the gantry rotatesthe kV imaging source and LINAC around an axis passing through theisocenter. Gantry-based systems include ring gantries having generallytoroidal shapes in which the patient's body extends through the bore ofthe ring/toroid, and the kV imaging source and LINAC are mounted on theperimeter of the ring and rotates about the axis passing through theisocenter. Gantry-based systems may further include C-arm gantries, inwhich the kV imaging source and LINAC are mounted, in a cantilever-likemanner, over and rotates about the axis passing through the isocenter.In another embodiment, the kV imaging source and LINAC may be used in arobotic arm-based system, which includes a robotic arm to which the kVimaging source and LINAC are mounted as discussed above.

FIG. 6 illustrates a gantry based intensity modulated radiationtreatment (IMRT) system 709, in accordance with implementations of thepresent disclosure. In gantry based system 709, a radiation source(e.g., a LINAC 1201) having a head assembly 701 is mounted on a gantry703. In one embodiment, radiation beams 160 may be delivered fromseveral positions on a circular plane of rotation (e.g., around an axisof rotation). In one embodiment, system 709 includes a treatment imagingsystem, which may include a kV imaging source 705 and an x-ray detector707. The kV imaging source 705 may be used to generate x-ray images of aregion of interest (ROI) of patient by directing a sequence of x-raybeams at the ROI which are incident on the x-ray detector 707 oppositethe kV imaging source 705 to image the patient for setup and generatein-treatment images. The resulting system generates arbitrarily shapedradiation beams 760 that intersect each other at an isocenter to delivera dose distribution to the target location. In one implementation, thegantry based system 700 may be a c-arm based system.

FIG. 7 illustrates a helical radiation delivery system 800 in accordancewith embodiments of the present disclosure. The helical radiationdelivery system 800 may include a linear accelerator (LINAC) 810 mountedto a ring gantry 820. The LINAC 810 may be used to generate a narrowintensity modulated pencil beam (i.e., treatment beam) by directing anelectron beam towards an x-ray emitting target. The treatment beam maydeliver radiation to a target region (i.e., a tumor). The ring gantry820 generally has a toroidal shape in which the patient 830 extendsthrough a bore of the ring/toroid and the LINAC 810 is mounted on theperimeter of the ring and rotates about the axis passing through thecenter to irradiate a target region with beams delivered from one ormore angles around the patient. During treatment, the patient 830 may besimultaneously moved through the bore of the gantry on treatment couch840.

The helical radiation delivery system 800 includes a treatment imagingsystem, which may include a kV imaging source 850 and an x-ray detector870. The kV imaging source 850 may be used to generate x-ray images of aregion of interest (ROI) of patient 830 by directing a sequence of x-raybeams at the ROI which are incident on the x-ray detector 870 oppositethe kV imaging source 850 to image the patient 830 for setup andgenerate in-treatment images. The treatment imaging system may furtherinclude a collimator 860. In one embodiment, the collimator 860 may be avariable aperture collimator. In another embodiment, the collimator 860may be a multi-leaf collimator (MLC). The MLC includes a housing thathouses multiple leaves that are movable to adjust an aperture of the MLCto enable shaping of an imaging x-ray beam. In another embodiment, thevariable aperture collimator 860 may be an iris collimator containingtrapezoidal blocks that move along a frame in a manner similar to acamera iris to produce an aperture of variable size that enables shapingof the imaging x-ray beam. The kV imaging source 850 and the x-raydetector 870 may be mounted orthogonally relative to the LINAC 810(e.g., separated by 90 degrees) on the ring gantry 820 and may bealigned to project an imaging x-ray beam at a target region and toilluminate an imaging plane of detector 870 after passing through thepatient 130. In some embodiments, the LINAC 810 and/or the kV imagingsource 850 may be mounted to a C-arm gantry in a cantilever-like manner,which rotates the LINAC 810 and kV imaging source 850 about the axispassing through the isocenter. Aspects of the present disclosure mayfurther be used in other such systems such as a gantry-based LINACsystem, static imaging systems associated with radiation therapy andradiosurgery, proton therapy systems using an integrated image guidance,interventional radiology and intraoperative x-ray imaging systems, etc.

Helical radiation delivery system 800 includes also includes a secondaryimaging system 801. Imaging system 801 is a CBCT imaging system, forexample, the medPhoton ImagingRing System. Alternatively, other types ofvolumetric imaging systems may be used. The secondary imaging system 801includes a rotatable gantry 807 (e.g., a ring) attached to an arm andrail system (not shown) that move the rotatable gantry 807 along one ormore axes (e.g., along an axis that extends from a head to a foot of thetreatment couch 840. An imaging source 803 and a detector 805 aremounted to the rotatable gantry 807. The rotatable gantry 807 may rotate360 degrees about the axis that extends from the head to the foot of thetreatment couch. Accordingly, the imaging source 803 and detector 805may be positioned at numerous different angles. In one embodiment, theimaging source 803 is an x-ray source and the detector 805 is an x-raydetector. In one embodiment, the secondary imaging system 801 includestwo rings that are separately rotatable. The imaging source 803 may bemounted to a first ring and the detector 805 may be mounted to a secondring.

FIG. 8 illustrates examples of different systems 600 within which a setof instructions, for causing the systems to perform any one or more ofthe methodologies discussed herein, may be executed. In alternativeimplementations, the machine may be connected (e.g., networked) to othermachines in a local area network (LAN), an intranet, an extranet, and/orthe Internet. Each of the systems may operate in the capacity of aserver or a client machine in client-server network environment, as apeer machine in a peer-to-peer (or distributed) network environment, oras a server or a client machine in a cloud computing infrastructure orenvironment.

The example radiation treatment delivery system 100, which may representtreatment delivery systems 1200, 800, 709, or some other system,includes a processing device 602, a main memory (e.g., read-only memory(ROM), flash memory, dynamic random access memory (DRAM) such assynchronous DRAM (SDRAM) or Rambus DRAM (RDRAM), etc.), a static memory(e.g., flash memory, static random access memory (SRAM), etc.), and adata storage device, which communicate with each other via a bus.

The systems are machines capable of executing a set of instructions(sequential or otherwise) that specify actions to be taken by thatmachine. Further, while a single machine is illustrated, the term“machine” shall also be taken to include any collection of machines thatindividually or jointly execute a set (or multiple sets) of instructionsto perform any one or more of the methodologies discussed herein.

FIG. 8 illustrates examples of different systems 600 within which a setof instructions, for causing the systems to perform any one or more ofthe methodologies discussed herein, may be executed. In alternativeimplementations, the machine may be connected (e.g., networked) to othermachines in a local area network (LAN), an intranet, an extranet, and/orthe Internet. Each of the systems may operate in the capacity of aserver or a client machine in client-server network environment, as apeer machine in a peer-to-peer (or distributed) network environment, oras a server or a client machine in a cloud computing infrastructure orenvironment.

The example radiation treatment delivery system 100, which may representtreatment delivery systems 1200, 800, 709, or some other system,includes a processing device 602, a main memory (e.g., read-only memory(ROM), flash memory, dynamic random access memory (DRAM) such assynchronous DRAM (SDRAM) or Rambus DRAM (RDRAM), etc.), a static memory(e.g., flash memory, static random access memory (SRAM), etc.), and adata storage device, which communicate with each other via a bus.

Processing device 602 represents one or more general-purpose processingdevices such as a microprocessor, a central processing unit, or thelike. Processing device may be the same or a different processing deviceas processing device 1230 and may also represent the processing devicein treatment delivery workstation 150. More particularly, the processingdevice may be complex instruction set computing (CISC) microprocessor,reduced instruction set computing (RISC) microprocessor, very longinstruction word (VLIW) microprocessor, or processor implementing otherinstruction sets, or processors implementing a combination ofinstruction sets. Processing device 602 may also be one or morespecial-purpose processing devices such as an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA), adigital signal processor (DSP), network processor, or the like. Theprocessing device 602 is configured to execute instructions forperforming the operations and steps discussed herein.

The computer system 600 may further include a network interface deviceto communicate over the network. The computer system 600 also mayinclude a video display unit (e. g., a liquid crystal display (LCD) or acathode ray tube (CRT)), an alphanumeric input device (e. g., akeyboard), a cursor control device (e. g., a mouse), a graphicsprocessing unit, a signal generation device (e.g., a speaker), graphicsprocessing unit, video processing unit, and audio processing unit.

The data storage device 618 may include a machine-readable storagemedium 624 (also known as a computer-readable medium) on which is storedone or more sets of instructions or software 626 embodying any one ormore of the methodologies or functions described herein. Theinstructions 626 may also reside, completely or at least partially,within the main memory 604 and/or within the processing device 602during execution thereof by the computer system 600, the main memory 604and the processing device 602 also constituting machine-readable storagemedia.

In one implementation, the instructions 626 include an x-ray motioncomponent to implement functionality corresponding to the disclosureherein. While the machine-readable storage medium is shown in an exampleimplementation to be a single medium; the term “machine-readable storagemedium′ should be taken to include a single medium or multiple media(e.g., a centralized or distributed database, and/or associated cachesand servers) that store the one or more sets of instructions. The term“machine-readable storage medium” shall also be taken to include anymedium that is capable of storing or encoding a set of instructions forexecution by the machine and that cause the machine to perform any oneor more of the methodologies of the present disclosure. The term“machine-readable storage medium” shall accordingly be taken to include,but not be limited to, solid-state memories, optical media and magneticmedia.

It will be apparent from the foregoing description that aspects of thepresent disclosure may be embodied, at least in part, in software. Thatis, the techniques may be carried out in a computer system or other dataprocessing system in response to a processing device 625, 640, or 602(see FIG. 8), for example, executing sequences of instructions containedin a memory. In various implementations, hardware circuitry may be usedin combination with software instructions to implement the presentdisclosure. Thus, the techniques are not limited to any specificcombination of hardware circuitry and software or to any particularsource for the instructions executed by the data processing system. Inaddition, throughout this description, various functions and operationsmay be described as being performed by or caused by software code tosimplify description. However, those skilled in the art will recognizewhat is meant by such expressions is that the functions result fromexecution of the code by processing device 625, 640, or 602.

A machine-readable medium can be used to store software and data whichwhen executed by a general purpose or special purpose data processingsystem causes the system to perform various methods of the presentdisclosure. This executable software and data may be stored in variousplaces including, for example, system memory and storage or any otherdevice that is capable of storing at least one of software programs ordata. Thus, a machine-readable medium includes any mechanism thatprovides (i.e., stores) information in a form accessible by a machine(e.g., a computer, network device, personal digital assistant,manufacturing tool, any device with a set of one or more processors,etc.). For example, a machine-readable medium includesrecordable/non-recordable media such as read only memory (ROM), randomaccess memory (RAM), magnetic disk storage media, optical storage media,flash memory devices, etc. The machine-readable medium may be anon-transitory computer readable storage medium.

Unless stated otherwise as apparent from the foregoing discussion, itwill be appreciated that terms such as “receiving,” “positioning,”“performing,” “emitting,” “causing,” or the like may refer to theactions and processes of a computer system, or similar electroniccomputing device, that manipulates and transforms data represented asphysical (e.g., electronic) quantities within the computer system'sregisters and memories into other data similarly represented as physicalwithin the computer system memories or registers or other suchinformation storage or display devices. Implementations of the methodsdescribed herein may be implemented using computer software. If writtenin a programming language conforming to a recognized standard, sequencesof instructions designed to implement the methods can be compiled forexecution on a variety of hardware platforms and for interface to avariety of operating systems. In addition, implementations of thepresent disclosure are not described with reference to any particularprogramming language. It will be appreciated that a variety ofprogramming languages may be used to implement implementations of thepresent disclosure.

It should be noted that the methods and apparatus described herein arenot limited to use only with medical diagnostic imaging and treatment.In alternative implementations, the methods and apparatus herein may beused in applications outside of the medical technology field, such asindustrial imaging and non-destructive testing of materials. In suchapplications, for example, “treatment” may refer generally to theeffectuation of an operation controlled by the treatment planningsystem, such as the application of a beam (e.g., radiation, acoustic,etc.) and “target” may refer to a non-anatomical object or area.

In the foregoing specification, the disclosure has been described withreference to specific exemplary implementations thereof. It will,however, be evident that various modifications and changes may be madethereto without departing from the broader spirit and scope of thedisclosure as set forth in the appended claims. The specification anddrawings are, accordingly, to be regarded in an illustrative senserather than a restrictive sense.

What is claimed is:
 1. A method, comprising: generating a plurality oftwo dimensional projections of an internal target region within a bodyof a patient, the plurality of two dimensional projections comprisingtwo dimensional projection data about a two dimensional position of aninternal target region of the patient, wherein each of the plurality oftwo dimensional projections are generated sequentially at differentpoints in time; generating external positional data about externalmotion of the body of the patient using one or more external sensors;generating, by a processing device, a correlation model between theexternal positional data and a three dimensional position of theinternal target region by directly fitting, in two dimensions, theplurality of two dimensional projections of the internal target region,generated sequentially at different points in time, to the externalpositional data, wherein directly fitting the plurality of twodimensional projections of the internal target region to the externalpositional data comprises identifying a best fit of an analytic functionwith respect to the plurality of two dimensional projections and theexternal positional data, wherein the analytic function projects a threedimensional position into two dimensions; and estimating the threedimensional position of the internal target region at a later time usingthe correlation model.
 2. The method of claim 1, wherein the pluralityof two dimensional projections is sequentially acquired monoscopicprojection images acquired using an imager rotated on a gantry.
 3. Themethod of claim 1, wherein the two dimensional projection dataidentifies internal motion of the patient's body, the internal motioncomprising motion of the internal target region.
 4. The method of claim1, wherein the two dimensional projection data identifies internalmotion of the patient's body, the internal motion comprising motion ofone or more implanted fiducial markers.
 5. The method of claim 1, themethod further comprising: directing a radiation treatment beamgenerated by a linear accelerator (LINAC) based on the correlationmodel.
 6. The method of claim 1 the method further comprising:controlling a collimator of a linear accelerator (LINAC) based on thecorrelation model.
 7. The method of claim 6, wherein the collimator is amulti-leaf collimator and to control the collimator, the methodcomprising moving one or more leafs of the multi-leaf collimator.
 8. Themethod of claim 1, the method further comprising: controlling atreatment couch.
 9. The method of claim 1, the method furthercomprising: gating a radiation treatment beam generated by a linearaccelerator (LINAC) based on the correlation model.
 10. The method ofclaim 1, wherein the projection data corresponds to one or more fiducialmarkers located near the internal target region, wherein to generate thecorrelation model the method further comprising: computing a deformationstate of the internal target region based on relative positions of theone or more fiducial markers.
 11. A radiation treatment deliveryapparatus, comprising: a first detection device to generate twodimensional projection data about a target region internal to a body ofa patient, wherein the two dimensional projection data comprises twodimensional projections generated sequentially at different points intime; a second detection device to generate positional data about one ormore sensors external to the body of the patient; and a processingdevice to receive the two dimensional projection data about the internaltarget region and the positional data from the external sensors andgenerate a correspondence between the positional data and a threedimensional position of the internal target region by directly fittingthe two dimensional projection data of the internal target region,generated sequentially at different points in time, to the externalsensors to control the radiation treatment delivery apparatus based onthe position data obtained from the external sensors to compensate formotions of the patient, wherein directly fitting the two dimensionalprojections of the internal target region to the external sensorscomprises identifying a best fit of an analytic function with respect tothe two dimensional projections and the external sensors, wherein theanalytic function projects a three dimensional position into twodimensions.
 12. The apparatus of claim 11, wherein the first detectiondevice comprises a rotatable single imager.
 13. The apparatus of claim12, further comprising a linear accelerator (LINAC) comprising anonboard kilovoltage (kV) imager coupled to a gantry, wherein the firstdetection device is coupled to the gantry.
 14. The apparatus of claim11, wherein the first detection device is further to: generate aplurality of sequential images; and generate a single projection basedon the plurality of sequential images.
 15. The apparatus of claim 11,further comprising a linear accelerator (LINAC) coupled to a moveablestage, wherein the first detection device comprises a cone-beam CT(CBCT) imager coupled to a gantry.
 16. The apparatus of claim 15,wherein the moveable stage is the gantry.
 17. The apparatus of claim 15,wherein the moveable stage is separate from the gantry.
 18. Theapparatus of claim 15, wherein the correspondence between the positionaldata and three dimensional position of the internal target region isgenerated during acquisition of a CBCT scan.
 19. The apparatus of claim15, wherein the first detection device comprises a portal imager.
 20. Anon-transitory computer readable medium comprising instructions that,when executed by a processing device of a radiation treatment deliverysystem, cause the processing device to: generate a plurality of twodimensional projections of an internal target region within a body of apatient, the plurality of two dimensional projections comprising twodimensional projection data about a two dimensional position of aninternal target region of the patient, wherein each of the plurality oftwo dimensional projections are generated sequentially at differentpoints in time; generate external positional data about external motionof the body of the patient using one or more external sensors; generate,by the processing device, a correlation model between the externalpositional data and a three dimensional position of the internal targetregion by directly fitting, in two dimensions, the plurality of twodimensional projections of the internal target region generatedsequentially at different points in time to the external positionaldata, wherein directly fitting the plurality of two dimensionalprojections of the internal target region to the external positionaldata comprises identifying a best fit of an analytic function withrespect to the plurality of two dimensional projections and the externalpositional data, wherein the analytic function projects a threedimensional position into two dimensions; and estimate the threedimensional position of the internal target region at a later time usingthe correlation model.
 21. The non-transitory computer readable mediumof claim 20, wherein the plurality of projections is sequentiallyacquired monoscopic projection images acquired using an imager rotatedon a gantry.
 22. The non-transitory computer readable medium of claim20, wherein the two dimensional projection data identifies internalmotion of the patient's body, the internal motion comprising motion ofthe internal target region.
 23. The non-transitory computer readablemedium of claim 20, wherein the two dimensional projection dataidentifies internal motion of the patient's body, the internal motioncomprising motion of one or more implanted fiducial markers.
 24. Amethod, comprising: sequentially acquiring a plurality of twodimensional x-ray images of a target using a single imager on a rotatinggantry by rotating the single imager around the target, wherein each ofthe plurality of two dimensional x-ray images are acquired sequentiallyat different points in time; and determining, by a processing device, athree dimensional position of the target directly using the sequentiallyacquired plurality of two dimensional x-ray images, wherein determiningthe three dimensional position of the target directly using thesequentially acquired plurality of two dimensional x-ray imagescomprises identifying a best fit of an analytic function with respect tothe plurality of two dimensional x-ray images, wherein the analyticfunction projects a three dimensional position into two dimensions. 25.The method of claim 24, further comprising controlling a radiationtreatment delivery system based on a correlation model.
 26. A method,comprising: generating two dimensional positional data about a twodimensional target position internal to a body of a patient, bygenerating a plurality of two dimensional projections of the twodimensional internal target position, wherein each of the plurality oftwo dimensional projections are generated sequentially at differentpoints in time; generating external positional data about externalmotion of the body of the patient using one or more external sensors,wherein the external positional data is generated more frequently thanthe plurality of two dimensional projections; and generating, by aprocessing device, a correspondence between the external positional dataand a three dimensional position of the target by directly fitting acorrelation model to the plurality of two dimensional projections of thetwo dimensional internal target position, generated sequentially atdifferent points in time, and the external positional data, whereinfitting the correlation model comprises identifying a best fit of ananalytic function with respect to the plurality of projections and theexternal positional data, wherein the analytic function projects a threedimensional position into two dimensions; and controlling a treatmentdelivery system to direct radiation towards the three dimensionalposition of the internal target position of the patient based thecorrelation model to compensate for motions of the patient.
 27. Themethod of claim 26, wherein the positional data corresponds to one ormore fiducial markers located near the internal target position, whereingenerating the correlation model comprises computing a deformation stateof the internal target position based on relative positions of the oneor more fiducial markers.